Learning target: I can organize, graph and calculate with spreading-time data, describe the shape of the relationship between temperature and spreading, and explain it with the average motion of particles.
Part A gives a class's results from timing how long one drop of dye takes to spread evenly through still water at six temperatures. You will calculate means, decide what to do with an unusual trial, graph the means and describe the shape of the graph. Part B gives results from a second test in which the water could not flow at all. Show every calculation. Round means to the nearest whole minute.
You will need: This worksheet, Pencil, Ruler, Calculator (optional)
A class filled tall 250 mL graduated cylinders with 200 mL of water at six temperatures (the teacher prepared and poured all the water), let each cylinder sit until the water was still, and added one drop of blue food dye to the center without stirring. They recorded the time until the color looked even from top to bottom against a white card. Each temperature was tested three times with fresh water.
| Water temperature (°C) | Trial 1 (min) | Trial 2 (min) | Trial 3 (min) | Mean (min) |
|---|---|---|---|---|
| 5 | 58 | 55 | 55 | |
| 15 | 41 | 38 | 41 | |
| 25 | 30 | 33 | 30 | |
| 35 | 26 | 24 | 12* | |
| 45 | 21 | 22 | 20 | |
| 55 | 18 | 19 | 20 |
Some of the spreading in a cylinder comes from gentle currents in the water. To remove them, a researcher used dishes of agar gel, a firm jelly that is almost entirely water but cannot flow. She placed one drop of dye on each dish, making a colored spot 5 mm across, covered the dishes, and kept them at four temperatures. After 6 hours she measured the width of the colored circle.
| Gel temperature (°C) | Width of colored circle after 6 hours (mm) |
|---|---|
| 5 | 14 |
| 20 | 17 |
| 35 | 19 |
| 50 | 22 |
To find a mean, add the trials and divide by how many you added. For 15 °C: 41 + 38 + 41 = 120, and 120 ÷ 3 = 40 minutes. If you leave out a trial, divide by the number of trials you kept. For the graph, put each temperature on the bottom axis and go straight up to the mean time; check your points by reading them back off the axes.
Warm water is also less 'sticky' than cold water: it flows more easily. Scientists say its viscosity is lower. Both faster particles and lower viscosity help dye spread faster in warm water. Design a test that could show whether temperature still matters when stickiness is held the same, for example by comparing water with a liquid that is thicker at the same temperature. Say what you would keep the same, what you would change, what you would measure, and what result would show that particle speed matters on its own.